This 1995 book delivers a quantitative account of the science of cosmology, designed for a non-specialist audience. The basic principles are outlined using simple maths and physics, while still providing rigorous models of the Universe. It offers an ideal introduction to the key ideas in cosmology, without going into technical details. The approach used is based on the fundamental ideas of general relativity such as the spacetime interval, comoving co-ordinates, and spacetime curvature. It provides a thoughtful discussion of the big bang, and the crucial questions of structure and galaxy formation. Questions of method and philosophical approaches in cosmology are also briefly discussed. This book will still be of value those interested physics and mathematics, particularly non-specialists.